Exploiting Superposition and Time-Invariance ∑ Linear system akin 1n=∑am k Question: Are there sets of basic signals so that a) We can represent rich classes of signals as linear combinations of these building block signals b) The response of lti systems to these basic signals are both simple and insightful Fact: For Lti Systems(Ct or dt) there are two natural choices for these building blocks Focus for now: dt Shifted unit samples Ct Shifted unit impulsesExploiting Superposition and Time-Invariance Question: Are there sets of “basic” signals so that: a) We can represent rich classes of signals as linear combinations of these building block signals. b) The response of LTI Systems to these basic signals are both simple and insightful. Fact: For LTI Systems (CT or DT) there are two natural choices for these building blocks Focus for now: DT Shifted unit samples CT Shifted unit impulses